In mathematics a **field of sets** is a pair where is a set and is an **algebra over ** i.e., a non-empty subset of the power set of closed under the intersection and union of pairs of sets and under complements of individual sets. In other words forms a subalgebra of the power set Boolean algebra of . (Many authors refer to itself as a field of sets. The word "field" in "field of sets" is not used with the meaning of field from field theory.) Elements of are called **points** and those of are called **complexes**.

Fields of sets play an essential role in the representation theory of Boolean algebras. Every Boolean algebra can be represented as a field of sets.

### Famous quotes containing the words field of, field and/or sets:

“A *field of* water betrays the spirit that is in the air. It is continually receiving new life and motion from above. It is intermediate in its nature between land and sky.”

—Henry David Thoreau (1817–1862)

“Every woman who visited the Fair made it the center of her orbit. Here was a structure designed by a woman, decorated by women, managed by women, filled with the work of women. Thousands discovered women were not only doing something, but had been working seriously for many generations ... [ellipsis in source] Many of the exhibits were admirable, but if others failed to satisfy experts, what of it?”

—Kate *Field* (1838–1908)

“Music *sets* up ladders,

it makes us invisible,

it *sets* us apart,

it lets us escape;

but from the visible

there is no escape.”

—Hilda Doolittle (1886–1961)